Foil shapes for use in barge skegs and marine propeller shrouds

ABSTRACT

An airfoil shape exhibiting low drag and a high lift/drag ratio has a low thickness/chord ratio and a low camber/chord ratio. The airfoil shape provides desirable results when used in barge skeg assemblies and in propeller shrouds for tugs used to tow ocean going barges.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of the filing date of co-pending U.S. Patent Application Ser. No. 61/134,220, filed Jul. 7, 2008.

BACKGROUND

The present disclosure relates to airfoil shapes and their utilization in propeller shroud or nozzle structures and in skeg arrangements for barges and other towed vessels having displacement hulls.

Gruzling U.S. Pat. No. 4,789,302 discloses the use of an airfoil shape in propeller shrouds to improve the efficiency of propeller performance by utilizing a nozzle section design providing for turbulent flow with a higher lift coefficient and lower drag coefficient than nozzles in use previously. Gruzling U.S. Pat. Nos. 4,217,844 and 4,569,302, and Heyrman et al. U.S. Pat. No. 4,782,779, disclose skeg arrangements for barges, in which airfoil shapes are utilized to improve water flow characteristics at the stem of a barge, in order to reduce yawing of a towed barge, thereby reducing the power required to tow the barge. When the barge tracks in line with the towing vessel less energy has to be utilized to turn the barge back into line and to tow the barge at an angle to the desired direction of advance.

SUMMARY OF DISCLOSURE

Disclosed herein and defined by the claims appended hereto are airfoil shapes for a skeg system and a propeller nozzle having improved performance characteristics and providing improved economy in use, by virtue of utilizing foil shapes and sizes resulting in less drag, together with greater lift.

In one embodiment a skeg system for a displacement hull of an ocean-going barge includes novel airfoil shapes with an improved lift/drag ratio in a skeg arrangement including horizontally-aligned and vertically-aligned foils.

In one embodiment of a skeg system for a barge, vertically-oriented skeg elements each lying in a vertical plane have a chord length that is smaller than the chord length of associated horizontally-oriented skeg elements. The vertically-oriented elements thus have less surface area and less surface drag while still producing sufficient laterally-directed lift forces to effectively reduce yawing of the barge during tow.

An airfoil shape for use in an embodiment of either the vertically-aligned or the horizontally-aligned elements of a skeg system may have a thickness-to-chord length ratio in the range of 13% to 20%.

In one embodiment an airfoil shape for use in either a vertically-aligned or a horizontally-aligned element of a skeg system may have a maximum ratio of camber to chord length in the range of 6.5% to 8%.

In one embodiment of a skeg system each vertically-aligned or horizontally-aligned skeg element may have a size providing a Reynolds number in the range of 1×10⁶ to 18×10⁶ for speeds in salt water in the range of 2-25 knots.

In one embodiment of a skeg arrangement for a barge, horizontally-aligned skeg foil elements having an airfoil shape of the type disclosed herein may be oriented at angles of attack in the range of −5 degrees to +5 degrees with respect to the slope of the surface of the underwater counter portion of the barge hull in order to provide a forwardly directed component of lift force generated by movement through water.

The foregoing and other features will be more readily understood upon consideration of the following detailed description of embodiments taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an isometric view of a barge under tow equipped with a skeg arrangement, taken from abaft the starboard quarter thereof.

FIG. 2 is a isometric view of a portion of the barge shown in FIG. 1 taken from a point below and off the starboard quarter of the barge shown in FIG. 1.

FIG. 3 is a side elevational view of the stem portion of a barge such as the one shown in FIG. 1, equipped with a skeg system incorporating the airfoil shapes disclosed herein.

FIG. 4 is a sectional view through the skeg system shown in FIGS. 1-3 taken along the line 4-4 of FIG. 3.

FIG. 5 is a detail view at an enlarged scale of the lower portion of the skeg arrangement shown in FIG. 3, taken along line 5-5 of FIG. 4, showing the shape and orientation of the horizontally-oriented foil.

FIG. 6 is a sectional view through a propeller shroud, showing an associated propeller and illustrating the foil shape utilized in the shroud.

FIG. 7 is a sectional view of a foil shape useful in connection with the skeg systems and propeller shroud disclosed herein.

DETAILED DESCRIPTION OF EMBODIMENTS

Referring now to the drawings which form a part of the disclosure herein, in FIG. 1 a barge 10 is shown at sea under tow. The barge 10 is being pulled by a tug (not shown) by means of a tow line attached to the bow 12 of the barge by a bridle 14.

At the stern 16 of the barge 10 a pair of skeg assemblies 18 are mounted beneath the water line 20 and extend downwardly away from a raked counter portion 22 of the hull of the barge 10, as may also be seen in FIGS. 2 and 3. There may be a separate skeg assembly 18 near each side of the stern 16 of the barge 10, as shown herein, or a unitary skeg assembly (not shown) may extend across the entire breadth of the stern 16.

As shown in FIGS. 2 and 3, the raked counter portion 22 of an oceangoing barge 10 may be generally flat and inclined upwardly from the extreme depth of the hull of the barge 10 toward the water line 20.

Each of the skeg assemblies 18 as shown herein includes three vertically oriented foil elements 24, 26, and 28, although a greater number or as few as two vertically oriented foil elements might be used. Each vertical foil element 24, 26, and 28 has an upper end 30 attached to and extending downwardly away from the raked counter portion 22. A bottom end 32 of each of the vertical foil elements is attached to a horizontally oriented foil element 36 by which each vertical foil element is interconnected with each of the other vertical foil elements 24, 26, and 28 of a skeg assembly 18. The horizontal foil element 36 may extend generally horizontally as seen from astern, with the length 38 of each of the vertical foil elements 24, 26, and 28 being as needed to extend parallel with the others from the horizontal foil element 36 to the bottom of the stern counter 22.

Each of the vertical foil elements 24, 26, 28 extends downwardly in a vertical plane from the raked counter portion 22 and may be oriented perpendicular to plane generally parallel to the bottom of the counter portion 22, as seen in profile in FIG. 3.

Each skeg assembly 18 may, as shown herein, extend over about one third of the breadth of the stem of the barge 10, or there may be a single skeg assembly (not shown) including a single horizontally oriented foil element extending over the entire breadth of the stern 16 and including additional vertical foil elements.

As may be seen in FIG. 4, each of the vertical foil elements 24, 26, and 28 has an airfoil section shape having a leading edge 40 forward, toward the bow 12 of the barge 10, and a trailing edge 42 toward the stern 16 of the barge 10. An airfoil shape in accordance with an embodiment of the present invention as will be disclosed subsequently herein provides a greater amount of such lift force with the same or a lesser amount of drag than has been heretofore known to be possible. As may be seen in FIG. 4, each of the vertical foil elements 24, 26, and 28 has a neutral axis or chord plane 43 defined between the leading edge 40 and the trailing edge 42, and each of the vertical foil elements 24, 26, and 28 is aligned at a selected angle of attack 44, 46, 48 defined between the chord plane 43 and a plane 50 parallel with a vertical centerline plane extending fore-and-aft with respect to the barge 10. Ideally the reference for foil orientation would be the free flow path of water around the hull of the vessel at the location of the foil element, but in practice the foils must be constructed by reference to the hull of the barge 10. The angles of attack 44, 46, and 48 may be such as to provide a desired amount of lateral force generated as lift by the airfoil shape. The angle of attack 44, 46, and 48 may thus range from −5 degrees to +5 degrees, to develop the lift force desired, while also limiting the resulting drag. Since the airfoil shape disclosed herein has a maximum lift/drag ratio at an angle of attack between −2 degrees and −4 degrees the angle of attack 44, 46, or 48 may be chosen in the range of 0 degrees to −5 degrees, or around −3 degrees, in one embodiment.

Each of the vertical foil elements 24, 26, and 28 has a chord length 54, between the respective leading edge 40 and trailing edge 42, and each of the vertical foil elements 24, 26, 28 is separated laterally from the next by a distance 60 which may be at least as great as the chord length 54. The vertical foil elements 24, 26, and 28 may be oriented so that the lift force L₁ generated by each of them is directed toward a centrally located vertical longitudinal plane defined by the barge 10. If the barge 10 yaws while being towed the vertical foil elements 24, 26, 28 on the side of the hull toward which the stem 16 has yawed will then be oriented so that the respective angles of attack of the vertical foil elements 24, 26, 28 are increased with respect to the direction toward the towing vessel and the actual flow of water past the vertical foil elements, thus providing an increased lift force L₁ directed laterally toward the centerline of the barge 10, to move the stern 16 of the barge 10 back toward the desired position and heading of the barge 10 astern of the towing vessel.

As may be seen in FIGS. 3 and 4, the horizontal foil element 36 is mounted at the bottom ends 32 of the vertical foil elements 24, 26, and 28. The horizontal foil element 36 has a leading edge 62, a trailing edge 64, a chord line or neutral plane 66 interconnecting the leading edge 62 and trailing edge 64, and a chord length 68 between the leading edge 62 and the trailing edge 64. The chord length 68 is at least as great as, and may be greater than the chord length 54 of the vertical foil elements 24, 26, and 28. For example, the chord length 68 may be as much as twice as great as the chord length 54. Where the chord length 68 is greater than the chord length 54 the vertical foil elements 24, 26, and 28 may be centered on the chord length of the horizontal foil element 36.

The horizontal foil element 36 may be oriented as seen in side view in FIG. 5 to establish an angle of attack 72 in the range of −5 degrees to +5 degrees, and optimally between −3 degrees and −4 degrees, relative to a plane H. Because of the direction of flow of water that has been displaced by the hull of the barge 10, as the barge 10 moves forward through the water, water flows generally parallel with the plane 74 parallel to the effective shape of the bottom surface of the raked counter 22, and upon encountering the horizontal foil element 36 creates a lift force L₂ generally perpendicular to the neutral plane 66. Because the neutral plane 66 is inclined forward below a horizontal plane H, at a negative angle 72 with respect to the horizontal plane H, the lift force L₂ has a forward component 78 tending to urge the barge 10 forward. So long as the size of the horizontal foil element 36 is small enough that the surface area doesn't generate too much drag and the Reynolds number is small enough, this forward component 78 of lift will reduce the amount of energy necessary to move the barge 10 forward through the water, contributing to fuel economy for towing the barge 10.

As shown in section view in FIG. 6, a propeller shroud 90 surrounds a propeller 92 carried on a propeller shaft 94. The propeller 92 as shown has 4 blades 96, one of which is shown in section view. An arrow 98 indicates the direction of movement of that blade when the propeller 92 is rotating in the usual direction in order to provide forward thrust through the shaft 94. It will be understood that propellers of various blade configurations might be used, and the propeller shown is merely one of several possibilities and not meant to be limiting.

The propeller 92 has a diameter 100, and the shroud 90 defines an interior diameter that is greater than the diameter 100 of the propeller 92 by a distance sufficient to assure that the interior surface 102 of the propeller shroud 90 will not be struck by the tip 122 of any of the blades 96 as the propeller 92 rotates. The clearance between the rotating blade tips 122 and the interior surface 102 of the propeller shroud is desirably kept as small as practical without unduly risking interference between the two, taking into consideration the expected flexure of the related structures.

In FIG. 6, the propeller shroud 90 is shown in section view. The shroud 90 has an outer surface 104 which defines, in cooperation with the interior surface 102, an airfoil shape having a leading edge 106 defining the circular forward end of the propeller shroud 90 and a trailing edge 108 defining the after end of the propeller shroud. The propeller shroud 90 thus acts as a nozzle with an inlet end 112, an outlet end 114, and a length 115 in the range of 0.3-0.6 times the diameter 100, and usually about equal to 0.5 times the diameter 100 of the propeller 92. At any point about the circumference of the shroud 90, a chord line or neutral axis 116 extending between the leading edge 106 and the trailing edge 108 of the airfoil sectional shape defines an angle of attack 118 with respect to a line parallel with the central axis 120 of the shroud, which is normally coincident with the axis of rotation of the shaft 94.

The sectional shape of the shroud is that of an airfoil that will be described in greater detail presently, with the interior surface 102 representing the upper surface of such an airfoil shape and the outer surface 104 being the lower surface of such an airfoil shape. The shroud 90 may normally be located with respect to the propeller blades 96 so that the tips 122 of the propeller blades 96 are aligned with the position C of the point of maximum camber of the airfoil shape. The resulting effect as a nozzle enables the propeller 92 to provide a greater propulsive force than would be possible without the shroud 90. The negative angle of attack 118 of the airfoil section shape allows more water to be drawn through the shroud 90 to be driven at a greater velocity by the propeller 92 than the propeller would be able to move effectively without the shroud 90.

Water drawn into the shroud 90 passes over the interior surface 102 of the shroud at an increased speed and reduced pressure, causing a net lift force L_(T) normal to the neutral axis 116. A net thrust component T of the lift force L_(T) urges the shroud forward, while the radially inward component of L_(T) essentially sums to zero. Using an airfoil shape such as is described below an angle of attack 118 as great as −8 degrees can be used to allow more water to enter the nozzle than is possible with previously known nozzles, in which the maximum angle of attack has been −6 degrees, without decreasing the lift force L_(T) to a useless amount.

An airfoil shape 130, shown in FIG. 7, is calculated to provide desirable lift and drag characteristics in the range of Reynolds numbers in which a skeg assembly 18 or a shroud 90 is likely to be used. The shape of the airfoil is defined, for one example, by the offsets listed in Table 1.

TABLE 1 Prototype AirFoil Offsets Section Longitudinal Location Displacement from Neutral Plane 1.00000000 0.00000000 0.99743466 0.00079972 0.98976497 0.00309903 0.97706963 0.00649761 0.95947891 0.01031398 0.93717331 0.01390046 0.91038172 0.01693123 0.87937905 0.01932935 0.84448345 0.02109677 0.80605298 0.02212220 0.76448199 0.02232138 0.72019708 0.02168834 0.67365266 0.02028115 0.62532633 0.01817777 0.57571398 0.01542160 0.52532470 0.01205427 0.47467554 0.00819478 0.42428620 0.00404683 0.37467374 −0.00019721 0.32634726 −0.00434447 0.27980269 −0.00826753 0.23551761 −0.01179841 0.19394647 −0.01480588 0.15551583 −0.01711130 0.12062003 −0.01855941 0.08961713 −0.01902380 0.06282523 −0.01839397 0.04051917 −0.01661490 0.02292769 −0.01373497 0.01023085 −0.00990420 0.00255744 −0.00556657 0.00000000 −0.00000000 0.00256992 0.00815640 0.01023689 0.01888232 0.02293198 0.03122573 0.04052255 0.04419256 0.06282795 0.05735818 0.08961929 0.07031909 0.12062167 0.08273630 0.15551698 0.09430334 0.19394717 0.10472343 0.23551791 0.11376513 0.27980274 0.12116876 0.32634717 0.12674560 0.37467355 0.13027027 0.42428597 0.13166384 0.47467532 0.13088411 0.52532453 0.12794693 0.57571386 0.12294330 0.62532625 0.11602893 0.67365262 0.10745297 0.72019708 0.09750468 0.76448201 0.08651320 0.80605299 0.07482401 0.84448346 0.06284826 0.87937906 0.05105590 0.91038172 0.03987534 0.93717331 0.02950656 0.95947891 0.01994017 0.97706963 0.01146193 0.98976497 0.00496561 0.99743466 0.00120015

The airfoil shape 130 includes a convex leading edge 132, a sharp trailing edge 134, an upper surface 136, a bottom surface 138, and a chord line or neutral axis 140 extending between the leading edge 132 and the trailing edge 134.

A chord length 142 is defined along the neutral axis 140 between the leading edge 132 and the trailing edge 134, and a maximum thickness 144 is in the range of 0.13 to 0.20 times the chord length 142. The maximum thickness 144 is located at a distance 146 from the leading edge that is within the range of 0.30 to 0.50 times the chord length 142.

The airfoil 130 has a maximum camber 150 in the range of 0.065 to 0.080 times the chord length 142, and the location of maximum camber is at a distance 152 from the leading edge 132 in the range of 0.35 to 0.55 times the chord length 142.

An airfoil defined by the offsets listed in Table 1 above is one example of an airfoil 130 within the parameters mentioned above and has a maximum thickness 144 of 0.131 times the chord length and located at a distance of 0.326 times the chord length 142 from the leading edge 132. It has a maximum camber of 0.065 times the chord length and located at a distance of 0.374 times the chord length 142 from the leading edge 132.

Using the airfoil shape 130 shown in FIG. 7 for the foil elements of a skeg assembly 18, with a chord length 142 of 2.5 ft. for each of the vertical foil members 24, 26, and 28 and a chord length 68 of 5 ft. for a horizontal foil element 36 and with a transverse length of the horizontal foil element 36 equal to 16 ft., a Reynolds number of about 3.5×10⁶ will result for the skeg assembly 18 at about 5 knots, as set out in Table 2 below.

Use of the airfoil shape 130 described above and in Table 1 for the vertically oriented skeg elements 24, 26, and 28 will, as shown in Table 2, provide a lesser drag yet a greater amount of lateral lift force L₁ to correct yawing of a barge 10 equipped with skeg assemblies 18 than has been possible using the previously known airfoil shapes for the components of such skeg assemblies, with high lift/drag ratios at various speeds, as may be calculated from Table 2 below.

TABLE 2 Skeg Assembly Using New Airfoil Section with Shorter Chord Length on Vertical Airfoil Sections Vertical Horizontal Section Vertical Section Horizontal Kinematic Chord Section Chord Section Reynolds Viscosity Density Length Length Speed Speed Length Length Number (Ft{circumflex over ( )}2/Sec) (lb-sec{circumflex over ( )}2/ft{circumflex over ( )}4) (Ft) (Ft) (ft/s) (Knots) (Ft) (Ft) 1.00E+06 1.28E−05 1.99 2.50 15.00 2.56 1.52 5.00 16.00 2.00E+06 1.28E−05 1.99 2.50 15.00 5.12 3.03 5.00 16.00 3.00E+06 1.28E−05 1.99 2.50 15.00 7.68 4.55 5.00 16.00 4.00E+06 1.28E−05 1.99 2.50 15.00 10.24 6.06 5.00 16.00 5.00E+06 1.28E−05 1.99 2.50 15.00 12.80 7.58 5.00 16.00 6.00E+06 1.28E−05 1.99 2.50 15.00 15.36 9.09 5.00 16.00 9.00E+06 1.28E−05 1.99 2.50 15.00 23.04 13.64 5.00 16.00 1.20E+06 1.28E−05 1.99 2.50 15.00 30.72 18.19 5.00 16.00 1.50E+06 1.28E−05 1.99 2.50 15.00 38.40 22.74 5.00 16.00 Lateral Total Lateral Vertical Lift Lift per Lift per per Total Total vertical 3 vertical horizontal Speed Total Area Cd Cl Drag Drag airfoil airfoils airfoil (Knots) (Ft{circumflex over ( )}2) (alfa = 0) (alfa = 0) (lbs) (HP) (lbs) (lbs) (lbs) 1.52 385 0.00688 1.0099 17 0.08 246.95 740.86 526.83 3.03 385 0.00585 1.0178 59 0.55 995.54 2986.61 2123.81 4.55 385 0.00544 1.0252 123 1.72 2256.24 6768.72 4813.31 6.06 385 0.00523 1.0293 210 3.91 4027.14 12081.41 8591.22 7.58 385 0.00510 1.0323 320 7.45 6310.74 18932.22 13462.91 9.09 385 0.00501 1.0346 453 12.65 9107.71 27323.13 19429.78 13.64  385 0.00487 1.0385 990 41.49 20569.60 61708.79 43881.81 18.19  385 0.00483 1.0398 1746 97.53 36613.95 109841.85 78109.76 22.74  385 0.00484 1.0404 2734 190.88 57242.31 171726.93 122116.93 Chord length for vertical sections, using the new airfoil section, has been reduced by a factor of ½. Calculated values for the drag show a reduction in drag for each vertical airfoil section while lateral lifting forces still remain higher than the NASA LS(1) airfoil section. This shows that new airfoil section creates equivalent lateral lifting forces with ½ the chord length which results in same directional stability to barge during tow but with reduced drag for skegs.

A shroud 90 manufactured using the airfoil shape 130 as defined above will also provide significantly improved thrust at a lesser investment of horsepower than required using previously known airfoil shapes for such shrouds.

The vertical foil elements 24, 26, and 28 and horizontal foil element 36 may be constructed, for example, in accordance with the methods described in U.S. Pat. No. 7,363,872.

Tank testing of models has shown surprisingly significant superiority in the ability of skeg systems utilizing airfoil shape disclosed herein, by comparison with those disclosed in Gruzling U.S. Pat. No. 4,217,844 and widely used in barges manufactured over the past twenty-plus years, to reduce yawing and lateral excursions of barges under tow in moderately loaded or fully loaded conditions and in sea states two to five.

While the skeg systems that have been modeled and tested have been designed with surface area equal or similar to that of the skeg systems of the commonly used Gruzling design built by NautiCan, indications based on model testing are that even better overall performance will be seen using skeg systems of similar design. Particularly in such skeg systems having reduced surface area, obtained by using a smaller number of vertical members, oriented to provide greater lateral lift force per vertical member, the desired yaw-opposing steering ability is expected to be obtained with less drag and thus with greater fuel economy while a barge so equipped is towed at higher speeds and in a more fully loaded, deeper draft condition.

The terms and expressions which have been employed in the foregoing specification are used therein as terms of description and not of limitation, and there is no intention in the use of such terms and expressions of excluding equivalents of the features shown and described or portions thereof, it being recognized that the scope of the invention is defined and limited only by the claims which follow. 

1. A skeg system for a barge, comprising: (a) at least a pair of vertically-oriented foil elements each having an upper end and a lower end; and (b) a horizontal foil element attached to and extending transversely between the vertical elements, wherein each of the vertical foil elements has a chord length and a thickness and the thickness is related to the chord length by a ratio in the range of 0.13 to 0.20, and wherein each of the vertical elements has a maximum camber, with a ratio of the maximum camber to the chord length in the range of 0.065 to 0.080.
 2. A skeg assembly for a barge, including at least a pair of vertical foil elements each disposed in a vertical plane and a horizontal element attached to and extending horizontally and transversely between the vertical foil elements, wherein each vertical foil element has a ratio of thickness to chord length (t/c) in the range of 0.13-0.20, and a ratio of maximum camber to chord length in the range of 0.065 to 0.080 and has a maximum thickness located at a distance from the leading edge in the range of 0.30 to 0.50 of the chord length.
 3. The skeg assembly of claim 2 wherein said vertical foil elements are oriented at an angle of attack in the range of −5° to +5° relative to a vertical plane parallel to a longitudinal centerline of the barge.
 4. The skeg assembly of claim 2 wherein the horizontal foil element is oriented at an angle of attack in the range of −5° to +5° relative to a plane parallel with a raked counter portion of a hull of the barge.
 5. The skeg assembly of claim 2 wherein the horizontal foil element has a chord length greater than the chord length of the vertical foil elements.
 6. The skeg assembly of claim 5 wherein the horizontal foil element has a chord length at least 1.25 times as great as the chord length of the vertical foil elements.
 7. The skeg assembly of claim 5 wherein the horizontal foil element has a chord length twice as great as the chord length of the vertical foil elements.
 8. The skeg assembly of claim 2 wherein the lift/drag ratio of each vertical foil element is at least 170 at a speed in salt water in the range of 5-15 knots.
 9. The skeg assembly of claim 2 wherein the horizontal foil element is oriented at an angle of attack, relative to a flow path of water already of the horizontal foil element beneath a raked counter portion of the barge, in the range of −5 to +5°.
 10. The skeg assembly of claim 9 wherein the angle of attack relative to the flow path is in the range of 0° to +5°.
 11. A propeller shroud for a marine propeller having a central shaft and plurality of radially extending blades, the shroud comprising: (a) a tubular nozzle structure having an interior surface shape and an exterior surface shape, the exterior and interior surface shapes cooperatively defining a foil section shape as seen in a radial plane extending through the tubular structure, the foil section shape having a thickness to chord length ratio in the range of 0.13 to 0.20, a camber to chord length ratio in the range of 0.65 to 0.080, with maximum camber located between 35% and 55% of the chord length from the leading edge; and wherein (b) the foil section shape has an angle of attack in the range of 0° to −8°.
 12. The propeller shroud of claim 11 wherein the angle of attack is in the range of −4° to −8°.
 13. The propeller shroud of claim 11 wherein the foil section shape of the tubular nozzle structure has a lift to drag ratio of at least 100 at an angle of attack within the range of 0° to −8° and operating at a Reynolds number in the range of 1×10⁶ to 18×00⁶.
 14. The propeller shroud of claim 11 wherein the drag coefficient (Cd) is in the range of 0.01-0.007 at speeds in salt water in the range of 5 knots-18 knots. 